The use of seismic surveys in the search for oil and gas reservoirs is commonplace. As is rudimentary in the art, seismic surveys are performed by imparting acoustic energy of a known amplitude and frequency pattern at one or more locations of the earth (either at a land surface or in a marine environment), followed by detecting reflected and refracted acoustic energy at other locations. The delay time between the imparting of the acoustic energy at the source location and detection of the same wave at a receiver location is indicative of the depth at which a particular reflecting geological interface is located. The field of seismic data analysis is directed to techniques for analyzing the detected acoustic energy to determine both the location and also the properties of various geological strata.
Seismic energy propagates through the earth in one of two modes: compressional or “P” waves and shear or “S” waves, either of which may be generated by a wide variety of seismic sources. A known technique in the generation and analysis of conventional seismic surveys is referred to as amplitude variation with offset (“AVO”) analysis. Conventional AVO analysis of P-wave seismic data traces typically uses a three-term AVO equation that approximates the reflection coefficient R of the P-wave seismic data traces as a function of the angle of incidence θ, which is described asR≈P+G sin2θ+C sin2θtan2θ.  (1)
In this case, the attribute P is the zero-offset response, which may also be referred to as the AVO intercept. P is generally described as                     P        ≈                              1            2                    ⁢                                    (                                                                    Δ                    ⁢                                                                                  ⁢                                          V                      P                                                                            V                    P                                                  +                                  Δρ                  ρ                                            )                        .                                              (        2        )            
The coefficient G is referred to as the AVO slope or gradient, as it is representative of the rate of change of amplitude with the square of the angle of incidence. G is generally described as                     G        =                                            1              2                        ⁢                                          Δ                ⁢                                                                  ⁢                                  V                  P                                                            V                P                                              -                      2            ⁢                                          Δμ                                  ρ                  ⁢                                                                          ⁢                                      V                    p                    2                                                              .                                                          (        3        )            
C is the higher order AVO attribute and is generally described as:                     C        =                              1            2                    ⁢                                                    Δ                ⁢                                                                  ⁢                                  V                  P                                                            V                P                                      .                                              (        4        )            
In equations (2) through (4), VP is the average P-wave velocity, ρ is the average density, and ΔVP and Δρ are their respective contrasts. The term Δμ in equation (3) is the contrast in rigidity modulus.
The AVO intercept, AVO gradient and the AVO higher order attribute are generally derived by fitting Equation (1) to the P-wave seismic data traces using standard statistical curve fitting techniques, such as least square regression. Equation (1), however, does not take into account interference from signals reflected from nearby reflecting geological interfaces, thereby distorting the calculation of the AVO higher order attribute. Such interference generally occurs as a result of mode-converted reflections to the P-wave primary reflections. The effect of interference is particularly significant at long offsets, or large angles of incidence, e.g., greater than about 25 degrees.
Therefore, a need exists for a method and apparatus for performing AVO analysis of seismic data traces that takes into account the interference from signals reflected from nearby reflecting geological interfaces.